The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a ``butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.

中文翻译：

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2局部哈密顿量中的不对称蝴蝶速度

在具有局部相互作用的量子系统中，信息传播的速度是有限的。在许多这样的系统中，本地操作员会在时间上弹道扩散，并具有“蝴蝶速度”的特征，该速度可通过无序的相关函数来测量。通常，蝴蝶速度可以不对称地取决于方向在这项工作中，我们构建了一个简单的2局部哈密顿量族，以了解算子扩散的不对称流体动力学，我们的模型生活在一个一维晶格上，并且在左右空间方向之间表现出不对称的蝴蝶速度。在我们的模型哈密顿量的自由（非相互作用）极限中可以清楚地理解“蝴蝶”的速度，在该极限中，蝶形速度可以用准粒子速度来理解。